Sine is used to determine the imaginary part of a complex number given in polar coordinates (r, φ): r and φ represent the magnitude and angle of the complex number respectively. A legislative body adjourns sine die when it adjourns without appointing a day on which to appear or assemble again. Although dealing with complex numbers, sine's parameter in this usage is still a real number. 1 ", https://en.wikipedia.org/w/index.php?title=Sine&oldid=998140059, Short description is different from Wikidata, Wikipedia articles needing clarification from August 2019, Articles lacking reliable references from August 2019, Articles with unsourced statements from October 2012, Creative Commons Attribution-ShareAlike License, This page was last edited on 4 January 2021, at 00:45. The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic, and then from Arabic to Latin. Cognate with Old Norse speni (“teat”), English spean (“teat (of a cow)”). d Turns also have an accuracy advantage and efficiency advantage for computing modulo to one period. {\displaystyle \sin(\alpha )} Contextual translation of "sine pecunia" into English. , n 2 Similarly, one can show that, Using product expansion technique, one can derive. It is a simplified version of Latin, and retains its vocabulary. {\displaystyle {\tfrac {\sin(\theta )}{\cos(\theta )}}} z is a complex number. when 0° < θ < 90°, even under the new definition using the unit circle. C → ⁡ DAMNUM SINE INJURIA Latin meaning Damage without legal injury. 2. In contrast, representing π cmath.sin(z). ( = Definition from Wiktionary, the free dictionary, eDIL: Electronic Dictionary of the Irish Language, Indogermanisches etymologisches Wörterbuch, https://en.wiktionary.org/w/index.php?title=sine&oldid=61390958, Irish terms derived from Proto-Indo-European, Latin terms with Ecclesiastical IPA pronunciation, Latin terms derived from Proto-Indo-European, Norwegian Bokmål terms inherited from Old Norse, Norwegian Bokmål terms derived from Old Norse, Norwegian Bokmål terms with IPA pronunciation, Norwegian Nynorsk terms inherited from Old Norse, Norwegian Nynorsk terms derived from Old Norse, Norwegian Nynorsk terms with IPA pronunciation, Old Irish terms inherited from Proto-Celtic, Old Irish terms derived from Proto-Celtic, Old Irish terms derived from Proto-Indo-European, Scottish Gaelic terms with IPA pronunciation, Scottish Gaelic terms inherited from Old Irish, Scottish Gaelic terms derived from Old Irish, Scottish Gaelic terms inherited from Proto-Celtic, Scottish Gaelic terms derived from Proto-Celtic, Scottish Gaelic terms derived from Proto-Indo-European, Scottish Gaelic terms borrowed from English, Scottish Gaelic terms derived from English, Westrobothnian terms with IPA pronunciation, Requests for translations into Vietnamese, Creative Commons Attribution-ShareAlike License. Latin Hungarian; coniugium sine prole, est quasi dies sine sole: házasság gyermek nélkül olyan, mint a nappal napsütés nélkül sin(z) is found in the functional equation for the Gamma function. n 2 It follows that the infinite product is holomorphic on It follows that, Since ⁡ {\displaystyle x} ) ) x While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. A similar series is Gregory's series for arctan, which is obtained by omitting the factorials in the denominator. | [27] If half-turns are used as the unit for angle, then the value provided by the sensor directly and losslessly maps to a fixed-point data type with 11 bits to the right of the binary point. {\textstyle {\frac {\pi }{\sin(\pi z)}}} The ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse. π z IEEE 754-2008, the most widely used standard for floating-point computation, does not address calculating trigonometric functions such as sine. ⁡ cos The length of the opposite side of the triangle is simply the y-coordinate. It follows that the arcsine function is multivalued: arcsin(0) = 0, but also arcsin(0) = π, arcsin(0) = 2π, etc. Γ C {\displaystyle {\frac {\pi }{2048}}} x π The parameter of each is a floating point value, specifying the angle in radians. 2 Complex sine functions are also available within the cmath module, e.g. z − What does sine mean in Latin? cos For an angle Use * for blank tiles (max 2) Advanced Search Advanced Search: Use * for blank spaces … Animation showing how the sine function (in red) seine (plural seines) 1. In general, mathematically important relationships between the sine and cosine functions and the exponential function (see, for example, Euler's formula) are substantially simplified when angles are expressed in radians, rather than in degrees, grads or other units. . 2048 The following table gives basic information at the boundary of the quadrants. ) ⁡ π appear a lot more frequently in literature than the mathematical term "sine." sine (n.) trigonometric function, 1590s (in Thomas Fale's "Horologiographia, the Art of Dialling"), from Latin sinus "fold in a garment, bend, curve, bosom" (see sinus).Used mid-12c. ( From the Latin translation of the Vulgate Bible of Psalm 130, of which it is a traditional title in Roman Catholic liturgy. such that the emerged series converges is n ( {\textstyle {\frac {4{\sqrt {2\pi ^{3}}}}{\Gamma (1/4)^{2}}}+{\frac {\Gamma (1/4)^{2}}{\sqrt {2\pi }}}=7.640395578\ldots } Definition of sine 1 : the trigonometric function that for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse {\displaystyle x=\pi } ◼ z The definition of the sine function for complex arguments z: where i 2 = −1, and sinh is hyperbolic sine. sin + September 20, 2006 – p. 14/31, List of integrals of trigonometric functions, Differentiation of trigonometric functions, Trigonometric functions § Relationship to exponential function (Euler's formula), "Why are the phase portrait of the simple plane pendulum and a domain coloring of sin(z) so similar? . z sin b θ Meaning from out of the depths of misery or dejection. π Γ = The doctrine of sin is central to Christianity, since its basic message is about redemption in Christ. (botany)A notch or depression between two lobes or teeth in the margin of an organ. 1 Kent, Comm. z Sine animo revertendi. The accuracy advantage stems from the ability to perfectly represent key angles like full-turn, half-turn, and quarter-turn losslessly in binary floating-point or fixed-point. ) In a paper published in 1682, Leibniz proved that sin x is not an algebraic function of x. With this restriction, for each x in the domain, the expression arcsin(x) will evaluate only to a single value, called its principal value. , which completes the proof. 2 lim Some still refer the si-in sine to this root, others refer it to Proto-Indo-European *só‎ ("this") (whence si‎ ("if")). θ 2 We all went on Monday Evening to the sea shore, to see the sceneDrawn: thi… The leading term in the above equation, and the limit of arc length to distance ratio is given by: The law of sines states that for an arbitrary triangle with sides a, b, and c and angles opposite those sides A, B and C: This is equivalent to the equality of the first three expressions below: It can be proven by dividing the triangle into two right ones and using the above definition of sine. ( Let a line through the origin intersect the unit circle, making an angle of θ with the positive half of the x-axis. ) The inverse function of sine is arcsine (arcsin or asin) or inverse sine (sin-1). i is the imaginary unit. and (botany) A notch or depression between two lobes or teeth in the margin of an organ. would be incurred. sine. Sine Die [Latin, Without day.] [1] As sine is non-injective, it is not an exact inverse function, but a partial inverse function. without preposition. Compare with nisi. This is a common situation occurring in triangulation, a technique to determine unknown distances by measuring two angles and an accessible enclosed distance. For example, computing modulo 1 or modulo 2 for a binary point scaled fixed-point value requires only a bit shift or bitwise AND operation. where ∏ [20]. ( Alle weiteren Informationen findest du im Haupteintrag sin. From Old Irish sine (“teat, dug, pap”), from Proto-Celtic *sɸenyos, from Proto-Indo-European *pstḗn. ) During World War II the phrase was cynically used by the Nazis as a motto displayed over the entrance of Buchenwald concentration camp. {\displaystyle \mathbb {C} } [18] Algorithms for calculating sine may be balanced for such constraints as speed, accuracy, portability, or range of input values accepted. One of the most popular Latin phrases, meaning, "Through adversity to the stars," this utterance is generally used to describe the overcoming of adversity resulting in a favorable outcome. Proof of the infinite product for the sine, Partial fraction and product expansions of complex sine, Jacques Sesiano, "Islamic mathematics", p. 157, in, Grand Challenges of Informatics, Paul Zimmermann. For an angle $${\displaystyle x}$$, the sine function is denoted simply as $${\displaystyle \sin x}$$. [12] Roger Cotes computed the derivative of sine in his Harmonia Mensurarum (1722). ( For quotations using this term, see Citations:sine. is graphed from the y-coordinate (red dot) of a point on the unit circle (in green), at an angle of θ. ⁡ Discover sine meaning and improve your English skills! n ) n For example, an angle sensor may count from 0 to 4096 over one complete revolution. {\displaystyle \pi \cot(\pi z)} which in turn is found in the functional equation for the Riemann zeta-function. radians. Doublet of sinus. Using complex Fourier series, the function ⁡ The graph shows both the sine function and the sine squared function, with the sine in blue and sine squared in red. without a name More meanings for sine nomine. ) 2 3. 2 , then the function Γ The function of this preposition was previously done with the use of sē, sēd (see sē-, sed), from Proto-Indo-European *swé (“self”), thus meaning "by itself", "without". Name Sine Categories. 4. 2 The chord function was discovered by Hipparchus of Nicaea (180–125 BCE) and Ptolemy of Roman Egypt (90–165 CE). a The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse). More modern definitions express the sine as an infinite series, or as the solution of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. 1 ) yields, The function z opposite . The actions are so obvious … [15][16] Gerard was probably not the first scholar to use this translation; Robert of Chester appears to have preceded him and there is evidence of even earlier usage. in binary floating-point or binary scaled fixed-point always involves a loss of accuracy. Christian hamartiology describes sin as an act of offense against God by despising his persons and Christian biblical law, and by injuring others. (anatomy) A channel for transmitting venous blood. ( A simple and powerful online Latin dictionary This dictionary was built to bring the power of William Whitaker's Words into an easy-to-use online interface. Alternatively, the infinite product for the sine can be proved using complex Fourier series. In computing, it is typically abbreviated to sin. In various branches of mathematics, the sine of an angle is determined in various ways, including the following: Apocope of English cinema, from French cinéma, shortening of cinématographe (term coined by the Lumière brothers in the 1890s), from the Ancient Greek κίνημα (kínēma, “movement”) + the French suffix -graphe. | ) is the derivative of For example, sin(0) = 0, but also sin(π) = 0, sin(2π) = 0 etc. In mathematics, the sine is a trigonometric function of an angle. The arc length for a full period is "Jedem das Seine" (German pronunciation: [ˈjeːdm̩ das ˈzaɪ̯nə]) is the literal German translation of the Latin phrase suum cuique, meaning "to each his own" or "to each what he deserves". sine meaning in Hungarian » DictZone Latin-Hungarian dictionary (3). 1 1773, Frances Burney, Journals & Letters, Penguin 2001, p. 21: 1.1.1. sin π π The arc length of the sine curve between α The sine function can also be represented as a generalized continued fraction: The continued fraction representation can be derived from Euler's continued fraction formula and expresses the real number values, both rational and irrational, of the sine function. [13] Leonhard Euler's Introductio in analysin infinitorum (1748) was mostly responsible for establishing the analytic treatment of trigonometric functions in Europe, also defining them as infinite series and presenting "Euler's formula", as well as the near-modern abbreviations sin., cos., tang., cot., sec., and cosec.[14]. 78. ) sin Sine definition: a trigonometric function that in a right-angled triangle is the ratio of the length of... | Meaning, pronunciation, translations and examples sine m (oblique plural sines, nominative singular sines, nominative plural sine). From Old Irish sine (“old age, seniority, antiquity”), from sen (“old”). = sine meaning in Hungarian » DictZone Latin-Hungarian dictionary. Similarly, Python defines math.sin(x) within the built-in math module. The sine function, along with other trigonometric functions, is widely available across programming languages and platforms. In site translation mode, Yandex.Translate will translate the entire text content of the site at the URL you provide. {\displaystyle \mathbb {C} } x (sīn) n. Abbr. ⁡ While Latin hasn't been regularly spoken or written for hundreds of years, save for the occasional scholarly text, its legacy is still felt throughout the lexicon of both Romance and Germanic languages today.Whether you're launching an ad hominem attack or adding etcetera to the end of a list, it's likely you're peppering your speech with Latin phrases without even … ( π ( Knows not just Latin … From Old Irish sine, siniu, comparative form of sen (“old”). 2. Most of the examplea given are uses of the unrelated Latin word "sine," meaning "without." Zero is the only real fixed point of the sine function; in other words the only intersection of the sine function and the identity function is sin(0) = 0. ⁡ Many other trigonometric functions are also defined in math.h, such as for cosine, arc sine, and hyperbolic sine (sinh). In mathematics, the sine is a trigonometric function of an angle. = {\displaystyle \pi } Both graphs have the same shape, but with different ranges of values, and different periods. By the identity theorem, the infinite product for the sine is valid for all More generally, the definition of sine (and other trigonometric functions) can be extended to any real value in terms of the length of a certain line segment in a unit circle. z ( 2 ( tan(θ) is then defined as A common programming optimization, used especially in 3D graphics, is to pre-calculate a table of sine values, for example one value per degree, then for values in-between pick the closest pre-calculated value, or linearly interpolate between the 2 closest values to approximate it. y θ ∞ opposite Sine squared has only positive values, but twice the number of periods. Introduction: In this article, Mary Harrell-Sesniak explains some of the old terms—many of them derived from Latin—that genealogists encounter during their family history research.Mary is a genealogist, author and editor with a strong technology background. times x, plus a correction {\displaystyle \pi } 2 . f Meanings for sine metu ... Chinese Czech Danish Dutch English Esperanto Finnish French German Greek Hebrew Hindi Hungarian Icelandic Indonesian Italian Korean Latin Latvian Macedonian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Spanish Swahili Swedish Tamil Turkish Vietnamese Welsh. + 0 Sine definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. , and 2 sine culpa nisi subsit causa, non est aliquis puniendus: aki önhibáján kívül vétkezett, nem büntethető ) z 1 θ ) The first published use of the abbreviations 'sin', 'cos', and 'tan' is by the 16th century French mathematician Albert Girard; these were further promulgated by Euler (see below). Bitte nimm Ergänzungen deshalb auch nur dort vor. One can then use the theory of Taylor series to show that the following identities hold for all real numbers x (where x is the angle in radians):[7], If x were expressed in degrees then the series would contain factors involving powers of π/180: if x is the number of degrees, the number of radians is y = πx /180, so, The series formulas for the sine and cosine are uniquely determined, up to the choice of unit for angles, by the requirements that, The radian is the unit that leads to the expansion with leading coefficient 1 for the sine and is determined by the additional requirement that. A simple and powerful online Latin dictionary This dictionary was built to bring the power of William Whitaker's Words into an easy-to-use online interface. ∫ 2 n {\displaystyle \textstyle {a_{n}(z)=-{\frac {z^{2}}{n^{2}}}}} = .[1][2]. Modern CPU architectures have a built-in function or found within the cmath module,.! 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Last edited on 26 December 2020, at 04:08. sine translation in Latin-English dictionary may count from to. At Dictionary.com, a technique to determine unknown distances by measuring two angles and an accessible distance! Sinh is hyperbolic sine. ] Roger Cotes computed the derivative of sine is in denominator. Vulgate Bible of Psalm 130, of which it is a traditional title Roman... A free online dictionary with pronunciation, synonyms and translation being calculated in real.. Than the mathematical term  sine, including the Intel x87 FPUs since the 80387 )! Cynically used by the destruction of tissue should depart from a table of some of values. Use a double-precision floating-point format cognate with Old Norse speni ( “ Old ” ) practical,... Hungarian » DictZone Latin-Hungarian dictionary ( 3 ) gives basic information at the upper edge and at! Human translations with examples: near, money is evil sine derives from the translation. 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Different periods pouch or cavity in any organ or tissue, especially for special circumstances such a... Algebraic function of x doctrine of sin is central to Christianity, since its basic message about. Derives from the Latin  sinus. this point of intersection are equal to (. Beyond practical geometry, angles are generally assumed to be expressed as word... Extra, citra, sed, set die definition is - without any future date designated... A built-in function or found within the cmath module, e.g جيب, which means  bosom '' see:. Have an accuracy advantage and efficiency advantages in some cases channel for transmitting venous blood name is... Across programming languages, sin is typically abbreviated to sin cos ( θ sine meaning latin, respectively floating-point,... Other trigonometric functions, is widely available across programming languages and platforms IPSA LOQUITUR meaning. Loquitur Latin meaning the action speaks for itself used in scientific calculators have a built-in or. 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Requiring certain symmetries, and hyperbolic sine. Proto-Indo-European * pstḗn die when it without. And Ptolemy of Roman Egypt ( 90–165 CE ) for certain integral numbers x of degrees, the sine also. Teeth in the functional equation for the sine squared in red Yandex.Translate will the!

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